Block approval voting explained

Block approval voting (also called unlimited voting, in reference to limited voting) is a winner-take-all system where each voter either approves or disapproves of each candidate, and the k candidates with the most approval votes win (where k is the predetermined committee size).^{[1] [2]} It does not provide proportional representation.

Example with comparison

Candidates are running in a 3 member district of the 10000 voters. Voters may not cast more than one vote for a single candidate.

• Under block approval voting (unlimited voting) voter may vote for any number of candidates.
• Under limited block approval voting voters may cast 6 votes maximum (twice as many as there are winners).
• Under (plurality) block voting, voters may cast 3 votes (but do not have to).
• Under the single non-transferable vote, voters may cast 1 vote.

Party A has about 35% support among the electorate (with one particularly well-like candidate), Party B around 25% (with two well-like candidates) and the remaining voters primarily support independent candidates, but mostly lean towards party B if they have to choose between the two parties. All voters vote sincerely, there is no tactical voting.

Candidate	Party		Block approval voting				Plurality block voting				Single non-transferable vote
			Votes	%	Elected?		Votes	%	Elected?		Votes	%	Elected?
Candidate A1		Party A	4200	42%	8.		3555	36%	3.		800	8%	4.
Candidate A2		Party A	4500	45%	5.		3700	37%	1.		1900	19%	1.
Candidate A3		Party A	3900	39%	9.		3600	36%	2.		700	7%	9.
Candidate B1		Party B	5200	52%	1.		2600	26%	4.		900	9%	3.
Candidate B2		Party B	5000	50%	2.		2500	25%	5.		1100	11%	2.
Candidate B3		Party B	4700	47%	4.		2400	24%	6.		400	4%	12.
Candidate I1		Independent	4400	44%	6.		2300	23%	8.		800	8%	4.
Candidate I2		Independent	4900	49%	3.		2395	20%	7.		800	8%	4.
Candidate I3		Independent	4400	44%	6.		1900	19%	9.		700	7%	7.
Candidate I4		Independent	3900	39%	9.		1800	15%	10		700	7%	7.
Candidate I5		Independent	2600	26%	11.		650	7%	11.		600	6%	10.
Candidate I6		Independent	2300	23%	12.		600	6%	12.		500	5%	11.

• Under the single non-transferable vote (not a type of approval voting), the 3 most popular candidates according to voters first preferences are elected, regardless of party affiliation.
• Under (plurality) block voting, the party with plurality support most likely wins all seats.
• Under limited block approval voting voters, voters of independent candidates may use their extra votes to help candidates other than their top 3, which may result in the reversal of the plurality block vote result.
• Under block approval voting, any party-affiliated or independent candidates particularly popular among the population may be elected, but it is possible that about half of the population can elect no representatives.

References

1. Fishburn . Peter C. . Little . John D. C. . May 1988 . An Experiment in Approval Voting . Management Science . en . 34 . 5 . 555–568 . 10.1287/mnsc.34.5.555 . 0025-1909.
2. Book: Lackner, Martin . Multi-Winner Voting with Approval Preferences . Skowron . Piotr . 2023 . Springer Nature . 978-3-031-09016-5 . English.